Member groups shouldn't say "private group" for logged in users

when a person marks the group as members only privacy, on the groups blocks it says "private group" but its not private. Its members only. Is it safe to change this text? Where do I change it to "members only"? Even members only can be confusing because people will think that it is for group members instead of site members. But if they see "private group", it is implied that it is completely private from outsiders and then I click on it and it let's me in. Confusing